DNS is essentially a database of IP addresses. Each IP address is a series of numbers that allow computers to communicate with each other. A website is identified on a server by its IP address. Instead of your visitors having to remember an IP address to type into their browser to access your site, they instead use your domain name. When your domain is entered into their browser, DNS translates it into an IP address because that is what computers understand.Your computer is able to connect to your web hosting and show your website on the browser once the IP address is found.
If you're having trouble finding a domain name (whether because of crowding or cyber-squatters), check for a help facility on each registrar's site. Domain registrars typically house search engines that return a listing of available names similar to the one you want. When you search for a domain name at Namecheap, for example, you get both the status of that name and a list of suffixes available for that name. Maybe [Sitename].com isn't available, but [Sitename].biz or .org is.